Chapter 2: Apendix

Question 1

How to compute expected value?

Answer 1

Loss %1 * Amount of Loss 1 + Loss %2 * Amount of loss 2….

Question 2

What does standard deviation mean in regards to uncertainty of loss?

Answer 2

The greater the standard deviation, the greater uncertainty of loss.

Question 3

How to calculate standard deviation?

Answer 3

(Amount of Loss1 - Amount of Loss 1)^2 (Probability of Loss1) + (Amount of Loss2 - Amount of Loss2)^2 (Probability of Loss2)…..= variance, Sqrt = SD

Question 4

What does the central limit theorem state?

Answer 4

The distribution of the sample mean will approach the normal distribution as the sample size increases

Question 5

What are the three probability distributions?

Answer 5

1. Binomial
2. Normal
3. Poisson

Question 6

When do you use the binomial probability distribution?

Answer 6

• Requires discrete variables (loss or no loss)
• Small number exposures

Question 7

When do you use the normal probability distribution?

Answer 7

• Normal
• More versatile
• More realistic
• Small number exposures

Question 8

When do you use the poisson probability distribution?

Answer 8

Use if exposure units are over 50 and probability of loss is very small

Question 9

In a normal probability distribution losses are arranged as:

Answer 9

• 68% of all losses will be within 1 standard deviation of the mean
• 95% of all losses will be within 2 standard deviations of the mean
• 99% of all losses will be within 3 standard deviations of the mean

Question 10

In binomial distribution what outcomes exist?

Answer 10

Loss or no loss

Question 11

How to calculate mean for binomial distribution?

Answer 11

n x p = mean

Question 12

What does the standard deviation of a binomial distribution measure?

Answer 12

risk or dispersion. For a binomial distribution, the standard deviation is, calculated by SQRT of N X P X Q

Question 13

What is underwriting risk?

Answer 13

When an insurance company increases the size of the sample insured, underwriting risk (maximum insured loss) increase because more insured exposure units could suffer a loss.

Question 14

How to calculate underwriting risk?

Answer 14

• Underwriting Risk = # of units insured x standard error of the avg. loss distribution
• n x 𝜎𝑥 or √𝑛x 𝜎x

n = # of units insured
𝜎𝑥 = standard error of a distribution
𝜎𝑥 = standard deviation of losses

Question 15

In a hard market how do underwriters act?

Answer 15

• Insurance companies raise their premiums or less coverage for the same premium
• More “conservative” in their underwriting
• Restricted contract provisions
• September 11 resulted in a hard market (large losses & bad investment returns

Question 16

In a soft market how do underwriters act?

Answer 16

• Insurance companies lower premiums
• More “liberal” underwriting
• Investment earnings exceed underwriting losses
• Deductibles are lower and contract terms are more attractive

Question 17

What is an example of a soft market insurance?

Answer 17

Life insurance

Question 18

What is an example of a hard market insurance?

Answer 18

Directors and officer’s liability insurance